The attractive force of gravity acts as a centripital force.
We know r and the gravitiational constant G, but we still need to find 
, the angular velocity of the Earth. Angular veloctiy is defined as anglular displacement divided by time, and we know how long it takes the Earth to revolve around the sun (1 year), so...
It takes 365 days for the Earth to go around the sun once. We need to change this to seconds so as to get SI units.
The actual mass of the sun is 
, less than 1% error!